adjacent segments together. This has the effect of simplifying the space of possible haplotypes so that a final set of sampling iterations can be carried out more efficiently. In practice, as we multiply these pruning and merging stages, the size of the model (i.e. the graphs) tend to converge as shown by the evolutions of the number of sites per segment (Supplementary Fig. 5a) and the total number of segments (Supplementary Fig. 5b).